The structural transformation and aggregate productivity in …web.iitd.ac.in/~debasis/Lectures_HUL737/papers/Aggregate... · 2016-01-22 · The structural transformation and aggregate

PEJ (2007) 6:23–46DOI 10.1007/s10258-006-0016-3

ORIGINAL ARTICLE

The structural transformation and aggregateproductivity in Portugal

Margarida Duarte · Diego Restuccia

Received: 29 March 2006 / Accepted: 21 November 2006 /Published online: 20 December 2006© Springer-Verlag 2006

Abstract We document the substantial process of structural transformation—the reallocation of labor between agriculture, manufacturing, and services—and aggregate productivity growth undergone by Portugal between 1956 and1995. We assess the quantitative role of sectoral labor productivity in account-ing for these processes. We calibrate a model of the structural transformationto data for the United States and use the model to gain insight into the factorsdriving the structural transformation and aggregate productivity growth inPortugal. The model implies that Portugal features low and roughly constantrelative productivity in agriculture and services (around 22%) and a modestbut growing relative productivity in manufacturing (from 44 to 110%). We findthat productivity growth in manufacturing accounts for most of the reductionof the aggregate productivity gap with the United States and that a furtherclosing of this gap can only be accomplished via improvements in the relativeproductivity of services.

JEL Classification O1 · O4

Keywords Structural transformation · Sectoral productivity

This paper was written while the authors were affiliated with the Federal Reserve Bank ofRichmond. We would like to thank the editor, two anonymous referees, and participants atthe Third Conference on Portuguese Economic Development in the European Contextorganized by the Bank of Portugal for their comments. All errors are our own.

M. Duarte (B) · D. RestucciaDepartment of Economics, University of Toronto, 150 St. George Street,Toronto, ON, Canada M5S 3G7e-mail: [email protected]

D. Restucciae-mail: [email protected]

24 M. Duarte, D. Restuccia

1 Introduction

We address the long-run economic performance of Portugal and its relationto the process of structural transformation. Between 1956 and 1995, Portugalreduced its aggregate labor productivity gap with the United States from 26 to53%.1 During the same time period, Portugal underwent a substantial processof structural transformation, whereby the agricultural sector was replacedin importance in a first stage by the manufacturing sector and in a secondstage by the service sector. In this paper, we assess the quantitative role ofsectoral productivity in accounting for the substantial process of structuraltransformation in Portugal and aggregate productivity growth relative to thatof the United States.

We develop a three-sector general-equilibrium model of the structuraltransformation following closely Rogerson (2005). In the model, labor re-allocation across sectors is driven by two channels: income effects due tonon-homothetic preferences as in Kongsamut, Rebelo and Xie (2001) and sub-stitution effects due to differential productivity growth across sectors as in Ngaiand Pissarides (2004). We calibrate the benchmark economy to the structuraltransformation of the United States between 1956 and 1995. We first use themodel to study the determinants of the process of structural transformationin Portugal during the same time period. We then assess the role of sectorallabor productivity growth in the process of structural transformation and inaggregate productivity growth in Portugal.2

We use the model calibrated to the US experience to restrict the levels ofsectoral labor productivity in Portugal relative to that in the United States in1956. We restrict these productivity differences so that the model is consistentwith the observed employment shares by sector and the level of relativeaggregate labor productivity in Portugal in this year. Together with the sectoralgrowth rates of labor productivity observed in the data between 1956 and 1995,we find that Portugal featured low and roughly constant relative productivity inagriculture and services (around 22%) and a modest but growing relative pro-ductivity in manufacturing (from 44 to 110%). In addition, Portugal featured atime-varying barrier to services. In the context of our model, we find that thesefeatures are essential in accounting for the process of structural transformationand the evolution of aggregate labor productivity in Portugal.

We then use the model of the structural transformation in Portugal toassess the quantitative role of sectoral labor productivity growth in the processof structural transformation and in the behavior of relative aggregate laborproductivity in Portugal. To do so, we perform a series of counterfactualexperiments whereby we replace a given observed sectoral labor productivitygrowth rate with a hypothetical one. Each counterfactual experiment has

1We measure labor productivity as gross domestic product (GDP) per worker.2The model allows us to isolate the contribution of sectoral productivity since shares of employ-ment are endogenous to productivity changes.

The structural transformation and aggregate productivity in Portugal 25

implications for the allocation of employment across sectors and relativeaggregate productivity. The analysis suggests that productivity growth in man-ufacturing accounts for most of the reduction in the aggregate productivity gapwith the United States between 1956 and 1995. Moreover, the model impliesthat improving labor productivity in the service sector would have large conse-quences for aggregate productivity in the context of the underlying structuraltransformation while leaving labor allocations roughly unchanged. In contrast,improving labor productivity in agriculture alone would have negligible effectson aggregate labor productivity while generating a substantial reallocationof labor out of agriculture. As a result, we find that when improvements inlabor productivity in agriculture and services are combined, the reallocation oflabor out of agriculture magnifies the aggregate productivity impact of laborproductivity in services.

Our paper is broadly related to a recent literature studying the evolutionof countries over time.3 In linking the process of structural transformationwith the evolution of aggregate productivity, our paper is closely related tothe study of regional convergence in the United States by Caselli and Coleman(2001) and to the study of cross-country income differences by Gollin, Parenteand Rogerson (2002). Our study differs from these papers in that we considerthree sectors of the economy and that we use the model to restrict sectoralproductivity differences between Portugal and the United States. Our paperis also related to Cavalcanti (2004) who studies business cycles in Portugaland Duarte and Restuccia (2006) who study productivity differences acrosscountries. Our focus in this paper is instead on the long-run evolution ofPortugal.

The paper is organized as follows. In the next section we document the long-run performance of the Portuguese economy relative to the United States andthe process of structural transformation in both countries. In Section 3, wedescribe the model. We calibrate the model in Section 4 and present the resultsin Section 5. We conclude in Section 6.

2 Transformation and long-run performance

In this section, we document the economic performance of Portugal relativeto that of the United States from 1950 to 2000 and the process of structuraltransformation in Portugal from 1956 to 1995 and in the United States from1869 to 1995.4

3See, for instance, Cole and Ohanian (1999) and Kehoe and Prescott (2002).4Later on in the paper we compare the long-run performance of Portugal relative to that of theUnited States from 1956 to 1995 due to data restrictions on sectoral employment.


2.1 The behavior of aggregate labor productivity

We focus on labor productivity as our measure of economic performance.5 Wefind a substantial process of convergence in aggregate labor productivity inPortugal relative to the United States from 1950 until the mid 1970s. However,this process slowed down considerably in the mid 1970s. (See Fig. 1.) Relativeaggregate labor productivity in Portugal increased steadily between 1950 and1975, from about 0.22 to 0.45. Between 1975 and 2000, relative GDP perworker in Portugal grew only 10 percentage points (from 0.45 to 0.55).6

To gain insight about the driving forces behind movements in output perworker we consider an aggregate production function that is common to bothcountries. Let output Y in a given country be characterized by a Cobb–Douglas

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ativ

e La

bor

Pro

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Fig. 1 Labor productivity in Portugal relative to the United States (Note: Labor productivity isGDP per worker from PWT6.1.)

5We refer to labor productivity, GDP per worker and output per worker interchangeably through-out the paper. We focus on trended data, obtained by applying the Hodrick–Prescott filter withsmoothing parameter λ = 100.6Relative aggregate labor productivity in Portugal was 0.26 in 1956 and 0.53 in 1995.


production function that depends on the total capital stock K, total hoursworked Lh, and total factor productivity (TFP) A:

Y = AKα (Lh)1−α . (1)

In this expression, L represents the number of workers employed, h representsaverage hours worked per employed person, and α represents the share ofpayments to capital in total income Y (when factor markets are competitive).Given observations on the capital stock, employment, hours worked, andoutput and given an estimate for the share of payments to capital in totalincome, we can obtain a measure of TFP (which is not directly observable inthe data) as the residual in Eq. 1.

We use Eq. 1 to write output per worker Y/L in its intensive form as:

YL

= A1

1−α

(KY

) α1−α

h. (2)

This equation shows that movements in GDP per worker Y/L can be decom-posed into movements in measured TFP, movements in the capital to outputratio K/Y, and movements in the average number of hours worked h.

Empirical evidence suggests that capital to output ratios are remarkablystable over time for many countries, including the United States and Portugal.7

As a result, we abstract from movements in the capital to output ratio as adriving force of relative GDP per worker between Portugal and the UnitedStates. In this section, we focus on the contribution of relative movements inmeasured TFP and hours worked in Portugal and the United States.8

In the United States, average hours worked per year fell from 2, 008 (about39 h/week) in 1950 to 1, 878 (about 36 h/week) in 2000. Thus, movements inhours worked contributed negatively towards growth in GDP per worker inthis period. In Portugal, average hours worked fell by more than in the UnitedStates between 1950 and 2000. Average hours worked were 2, 344 (about45 h/week) in 1950 and they fell to 1, 715 by 2000 (about 33 h/week). As aresult, the pattern of hours worked in Portugal relative to that of the UnitedStates suggests that hours worked contributed negatively towards the observedconvergence of relative GDP per worker.

Given the behavior of hours worked in Portugal relative to that of theUnited States over the period, we conclude that movements in productivity(measured TFP) were the main driving force behind the increase in relativeGDP per worker in Portugal (which more than offset the fall in relative hoursworked). We use this evidence to develop a model in Section 3 that emphasizesthe role of sectoral productivity on aggregate labor productivity. While thereare many potential sources of relative productivity movements across sectors(for instance, reallocation of capital, human capital and occupational choice,

7See, for instance, Kaldor (1961), Cooley and Prescott (1995), Kongsamut, Rebelo and Xie (2001)for the United States and Cavalcanti (2004) for Portugal.8We use data on hours per worker from the Conference Board and Groningen Growth andDevelopment Centre (2005), Total Economy Database.


among others), we abstract from these channels and focus attention on theimplications of sectoral productivity for the allocation of employment acrosssectors and aggregate productivity.

2.2 The process of structural transformation

The behavior of relative labor productivity in Portugal depicted in Fig. 1is associated with different patterns of labor productivity across sectors aswell as a substantial process of labor reallocation. This reallocation processfrom agriculture to manufacturing and from manufacturing into the servicesector is typically referred to in the development literature as the structuraltransformation of the economy.9

The process of structural transformation has been extensively documentedin the literature.10 This process is typically characterized by a substantial fall inthe share of employment in agriculture to less than 10%, by a steady increasein the share of employment in services, and by a hump-shaped pattern inthe share of employment in manufacturing. That is, the typical process ofstructural transformation involves an increase in the share of employment inmanufacturing in the early stages, followed by a decrease in the later stages.

Different economies have started the process of structural transformationat different points in time. In Fig. 2 we report the shares of employment inagriculture, manufacturing, and services in the United States from 1869 to1970, which are broadly consistent with the general characterization describedabove. By the middle of the twentieth century, a substantial degree of sectorallabor reallocation had already taken place in the United States. While in 1869the share of employment in agriculture, manufacturing, and services were0.48, 0.24, and 0.28, by 1948 these shares were 0.10, 0.34, and 0.56. In thesecond half of the century, the process of labor reallocation from agricultureand manufacturing into services continued (see first panel in Fig. 3). From1956 to 1995, the share of employment in agriculture in the United Statesfell from about 10% to about 3%, the share of employment in manufacturingfell from about 36% to 24%, while the share of employment in servicesincreased from 54% to 73%.11

Portugal has experienced a process of structural transformation that isbroadly consistent with the experience of other economies. Figure 3 (secondpanel) documents the share of employment in agriculture, manufacturing, andservices for Portugal from 1956 to 1995. Portugal has undergone a substantialprocess of sectoral labor reallocation in the last 50 years. The share of employ-ment in agriculture has fallen from 48% in 1956 to 12% in 1995. The share of

9In this paper we refer to manufacturing and industry interchangeably. In the Appendix wedescribe in detail our definition of sectors in the data.10See, for instance, Kuznets (1966), Maddison (1980), among others.11Figure 2 and the first panel in Fig. 3 use different data sources and the shares of employment for1956 do not match. Nevertheless, the two figures are consistent regarding the pattern of structuraltransformation in the United States.


1879 1899 1919 1929–37 1944–48 1953–57 1960–690

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Industry

Services

Fig. 2 Share of employment by sector in the United States (Note: The definition of employment ispersons engaged in production by sector from the U.S. Census Bureau, Department of Commerce(1975).)

employment in the service sector has increased steadily throughout this period,from 33% in 1956 to 65% in 1995. Similarly to other countries, the share ofemployment in manufacturing during this period has a hump-shaped pattern—it increased from 1956 to 1980 (from 19% to 26%) and decreased thereafter(to 23% in 1995). It is interesting to note that the structural transformationin Portugal from 1956 to 1995 resembles closely that of the United Statesbetween 1870 and 1956. Although Portugal started the process of structuraltransformation later than the United States, it has accomplished about thesame reallocation of labor across sectors in less than half the time (39 yearsin Portugal versus 89 years in the United States).

The evolution of employment across sectors observed in Portugal and theUnited States between 1956 and 1995 is associated with distinct patterns oflabor productivity across sectors. In the United States, labor productivityincreased in all sectors, specially so in agriculture, as shown in the third panelin Fig. 3. The annualized growth rates of labor productivity between 1956 and1995 were 3.8% in agriculture, 2.4% in manufacturing, and 1.5% in services.Sectoral labor productivity in Portugal between 1956 and 1995 is shown inthe fourth panel of Fig. 3. The annualized growth rates of labor productivity


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Years

Fig. 3 Share of employment and labor productivity by sector (Note: The series for the UnitedStates are obtained from the OECD Employment Database (2005) and the Conference Boardand Groningen Growth and Development Centre (2005) and the series for Portugal are obtainedfrom the Bank of Portugal. See the Appendix A for further details.)

over this period were 4.8% in manufacturing, 4.1% in agriculture, and 1.9% inservices.

From an accounting perspective, the patterns of labor productivity andshare of employment across sectors determine the behavior of aggregatelabor productivity. Since the shares of employment are endogenous to laborproductivity across sectors, in the following sections we develop a generalequilibrium model of the structural transformation and calibrate it to the USexperience. We use the calibrated model to asses the role of each sector in theprocess of structural transformation and in the behavior of relative aggregateproductivity in Portugal.

3 The model

We consider a simple model of the structural transformation of an economy asin Duarte and Restuccia (2006). The model follows closely Rogerson (2005).


At each date three goods are produced: agriculture, manufacturing, andservices. In the model, there are two sources of structural transformation: non-homothetic preferences and an elasticity of substitution between consumptionof manufacturing and service goods different from one.

3.1 Description of economic environment

3.1.1 Production

At each date there are three goods produced: agriculture (a), manufacturing(m), and services (s) according to the following constant returns to scaleproduction functions:

Yi = Ai Li, i ∈ {a, m, s}, (3)

where Yi is output in sector i, Li is labor allocated to production in sector i,and Ai is a sector-specific technology parameter.

3.1.2 Households

The economy is populated by an infinitely-lived representative householdof constant size over time. (Without loss of generality we normalize thepopulation size to one.) We assume that the household is endowed with oneunit of productive time each period that is supplied inelastically to the market.The household has preferences over consumption goods as follows:

∞∑t=0

β tu(ct, ca,t), β ∈ (0, 1),

where ca,t is the consumption of agricultural goods at date t and ct is theconsumption of a composite of manufacturing and service goods at date t. Theper-period utility is given by:

u(ct, ca,t) = log(ct) + V(ca,t),

where V(ca,t) is such that households only care to consume a subsistence levelof agricultural goods a.12 Formally, V(ca) = −∞ when ca < a, and V(ca) =min{ca, a} when ca ≥ a. This specification of preferences V makes our analysismuch more tractable. We show in Section 5 that this simple specification ofpreferences captures remarkably well the patterns of the share of employmentin agriculture observed in the data.

12The specification of preferences for agricultural goods featuring a subsistence level—i.e., alevel of consumption below which the household cannot survive—has a long tradition in thedevelopment literature. See, for instance, Echevarria (1997), Laitner (2000), Kongsamut et al.(2001), Caselli and Coleman (2001), Gollin et al. (2002), Restuccia, Yang and Zhu (2005),among many others. We follow Laitner (2000) and Gollin et al. (2002) in further simplifying thespecification of preferences for agriculture by assuming that households only care to consume thesubsistence level a.


The composite consumption ct is given by:

ct = [bcρ

m,t + (1 − b)(cs,t + s)ρ] 1

ρ ,

where s > 0, b ∈ (0, 1), and ρ < 1. Given s, these preferences imply that theincome elasticity of consumption of service goods is greater than one. Theparameter s can be interpreted as a constant level of production of servicegoods at home. Rogerson (2005) considers a generalization of this featurewhere people can allocate time to market and non-market production ofservice goods. However, we argue that our simplification is not as restrictiveas it may first appear since we abstract from labor hours in the model.

3.1.3 Market structure

We assume that there is a continuum of representative firms in each sector thatare competitive in output and factor markets. At each date, given the price ofgood-i output pi and wages w, a representative firm in sector i solves:

maxLi≥0

pi Ai Li − wLi, (4)

where Li is the demand for labor in sector i.The problem of the household is also static. At each date and given prices,

the household chooses consumption of each good to maximize the per-periodutility subject to the budget constraint. Formally,

maxci≥0

log[bcρ

m + (1 − b)(cs + s)ρ] 1

ρ + V(ca), (5)

subject topaca + pmcm + pscs = w.

In what follows we normalize the wage rate to one.

3.1.4 Market clearing

The demand for labor from firms must equal the exogenous supply of labor atevery date:

La + Lm + Ls = 1. (6)

Notice that labor inputs in the model Li can be associated with the shares ofemployment in the data. In addition, at each date the market for each goodproduced must clear:

ca = Ya, cm = Ym, cs = Ys. (7)

3.2 Equilibrium of the model

A competitive equilibrium is a set of prices {pa, pm, ps}, allocations {ca, cm, cs}for the household, and allocations {La, Lm, Ls} for firms such that: (a) givenprices, firm’s allocations {La, Lm, Ls} solve the firm’s problem in Eq. 4, (b)given prices, household’s allocations {ca, cm, cs} solve the household’s problemin Eq. 5, and (c) markets clear: Eqs. 6 and 7 hold.


The first order condition from the firm’s problem implies that the benefitand cost of a marginal unit of labor must be equal. Since the wage rate isnormalized to one, it follows that prices of goods are inversely related toproductivity:

pi = 1

Ai.

Our specification of V(ca) implies that ca = a and, therefore, labor in agricul-ture must satisfy:

La = aAa

. (8)

The first order conditions for consumption of manufacturing and service goodsimply:

b(1 − b)

(cm

cs + s

)ρ−1

= pm

ps.

Using the market clearing conditions for output in manufacturing and servicesand for labor we obtain:

Lm = (1 − La) + sAs

1 + x, (9)

where

x ≡(

b1 − b

) 1ρ−1

(Am

As

) ρ

ρ−1

,

and La is given by Eq. 8.Notice that when s = 0, Eq. 9 can be written as Ls/Lm = x. If, in addition,

ρ = 0, then the composite consumption good c is a Cobb–Douglas aggregate ofconsumption of manufacturing and service goods and differential productivitygrowth across these two sectors will cause no reallocation of labor. The elas-ticity of substitution between manufacturing and service goods ρ determineshow much relative labor productivity growth Am/As is needed to produce agiven reallocation of labor across sectors, for given s/As. For s = 0, the modelis consistent with labor reallocation from manufacturing into services as laborproductivity grows in the manufacturing sector relative to services if ρ < 0.When s is strictly positive, however, the model implies a given amount of laborreallocation from manufacturing into services as labor productivity in servicesgrows for higher elasticity of substitution ρ.

4 Calibration

We calibrate the benchmark economy to US data for the period from 1956to 1995. Our calibration strategy involves selecting parameter values so thatthe equilibrium of the model matches a given set of statistics in the data. Weshow that our simple framework captures the salient features of the structuraltransformation in the United States in this period.


Table 1 Parameter valuesand targets

Parameter Value Target US data

Ai,56 1.0 Normalization{Aa,t}95

t=57 {·} Labor productivity growth agriculture

{Am,t}95t=57 {·} Labor productivity growth industry

{As,t}95t=57 {·} Labor productivity growth services

a 0.10 Employment in agriculture 1956s 0.76 Employment in industry 1956b 0.04 Employment in industry 1957–1995ρ -1.5 Aggregate labor productivity growth

4.1 Description

We assume that a model period is one year. We need to select the followingparameters values: b , ρ, a, s, and the time series of productivity for eachsector Ai,t, i ∈ {a, m, s} and t from 1956 to 1995. Table 1 reports a summaryof calibrated parameters and targets.

Our calibration strategy is to restrict the parameters values to match thestructural transformation of the United States between 1956 and 1995. Sincein the model labor allocation in agriculture is determined independentlyof the state of the other sectors, the calibration procedure can be roughlydivided in two parts. First, we calibrate subsistence in agriculture so that theequilibrium of the model matches the share of employment in agriculture for1956. Second, we calibrate the other parameters of the model to match theshare of employment in manufacturing and aggregate productivity growth.

We proceed as follows. First, we normalize productivity levels across sectorsto one in 1956, i.e., Ai,56 = 1 for i ∈ {a, m, s}. Second, given our normalizationof productivity in 1956, we use data on labor productivity growth in theUnited States for each sector to obtain the time paths of productivity levels.13

Third, given the normalization Aa,56 = 1, we choose a to obtain the share ofemployment in agriculture in 1956 for the United States (see Eq. 8). Giventhe calibrated value for subsistence in agriculture, labor productivity growth inthis sector implies a share of employment in agriculture in the model that turnsout to be remarkably close to the time-series data for the United States. (SeeFig. 4.)

In the second component of the calibration, we restrict s, b , and ρ tomatch the share of employment in manufacturing over time and the annualizedgrowth rate of aggregate labor productivity. We proceed as follows. Given ρ

and b , s is chosen to match the share of employment in manufacturing forthe United States in 1956. Then b is chosen so that, given the time paths forlabor productivity in manufacturing and services, the model matches the timepath for the share of employment in manufacturing. Since ρ determines how

13The annualized growth rates of labor productivity between 1956 and 1995 for the United Statesare 3.8, 2.4 and 1.5% for agriculture, industry and services. Annualized growth rates between 1956

and 1995 are computed as γAi =(

Ai,95Ai,56

)1/39 − 1.


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Fig. 4 The structural transformation in the United States

much relative productivity growth is needed to produce a given reallocationof labor across sectors, ρ induces different patterns of aggregate productivitygrowth. We choose ρ to match average aggregate productivity growth duringthe period (at 1956 prices). We calculate from PWT6.1 that the annualizedgrowth rate of labor productivity in the United States between 1956 and 1995is 1.8%.

4.2 Results of the benchmark economy

Our calibration restricted preference and technology parameters of the modelto match some features of the data for the US structural transformationbetween 1956 and 1995. The shares of employment implied by the model arereported in Fig. 4 (dotted lines), together with data for the United States(solid lines). The equilibrium shares of employment across sectors impliedby the model match closely the process of structural transformation of theUnited States over this period. In particular, notice that although not explicitlycalibrated, the model matches well the time path for the share of employmentin agriculture. Also, the model implies a fall in the share of employment inmanufacturing from about 38% in 1956 to 26% in 1995, while the share ofemployment in services increases from about 53% to 72%. We found that,given the observed sectoral growth rates of labor productivity in the United


States, this process of labor reallocation between manufacturing and servicescould not be accomplished in the model without an income elasticity greaterthan one in services.14

5 Quantitative analysis

The calibrated benchmark economy imposes discipline on technology andpreference parameters. In this section, we use the model calibrated to theUnited States to perform experiments aimed at gaining insight into sectoralproductivity differences between Portugal and the United States and theprocess of structural transformation in Portugal. We then perform coun-terfactual exercises to assess the aggregate implications of different factorsdriving the process of structural transformation in Portugal. Our main findingsare that between 1956 and 1995 Portugal featured low and constant relative labor productivity in agriculture and services, and modest but growingrelative productivity in manufacturing. In addition, we show that, during theperiod, productivity growth in manufacturing accounts for a large portion ofthe reduction in the aggregate productivity gap with the United States and thatthe lack of relative productivity growth in services has kept Portugal laggingbehind in aggregate productivity relative to the United States.

5.1 Structural transformation in Portugal

We take four steps aimed at understanding the structural transformation inPortugal. First, we consider an economy identical to the benchmark economyin terms of preferences but featuring a lower initial level of economy-wideproductivity, consistent with the observation that output per worker in Portu-gal was 26% of the US level in 1956. Second, we allow for relative productivitydifferences across sectors in 1956 that are consistent with the observed sharesof employment in Portugal in this year. Third, we consider an economy inwhich, in addition to the features described above, productivity growth acrosssectors is driven by observations on sectoral productivity in Portugal. Finally,we consider a time-varying barrier to services that allows us to match the shareof employment in manufacturing in Portugal. In all these experiments, theparameter value for s is adjusted to the initial value of relative productivityin services for Portugal.15

14Alternatively, if we interpret s as being produced with a home technology, then we would requirea pattern for productivity growth in the home sector that depends on whether technologicalprogress is labor augmenting or labor saving. See the discussion in Rogerson (2005) and thedifferent approaches in Kongsamut et al. (2001) and Ngai and Pissarides (2004).15Although not explicitly modeled, one interpretation of s is as service goods produced at home.As a result, s cannot be invariant to large changes in productivity levels, such as those implied bythe analysis of the United States and Portugal.


5.1.1 Economy-wide productivity

The first experiment involves reducing labor productivity in every sector in1956 by a constant factor. As documented in Section 2, GDP per worker inPortugal in 1956 was 26% of GDP per worker in the United States. Hence,this experiment assumes that relative labor productivity in each sector was26%, i.e., Ai,56 = 0.26 for i ∈ {a, m, s}.16 For 1956, the model implies a share ofemployment in agriculture of 39% (48% in the data), a share of employmentin services of 31% (33% in the data), and a share of employment in industryof 30% (19% in the data). Hence, the model implies too little employment inagriculture and services and too much employment in manufacturing relativeto the data in 1956. These results suggest that Portugal may be less than 26%productive in agriculture and more than 26% productive in manufacturingin 1956 relative to the United States. We pursue this possibility in the nextexperiment.

5.1.2 Relative sectoral productivity in 1956

We set relative sectoral productivity in 1956 so that the model matchesthe shares of employment across sectors in Portugal for the same year (inaddition to the relative aggregate productivity of 26%). Our calibration of thisexperiment implies that agriculture, manufacturing, and services must be 22,44, and 22% as productive as in the benchmark economy in 1956.17 The resultsof this experiment in terms of the shares of employment across sectors arereported in Panel A of Fig. 5 where the solid lines represent the data and thedashed lines the model. Notice that the time path of the shares of employmentare different than in the data, specially in manufacturing and services.

5.1.3 Sectoral productivity growth

Portugal is not riding along the same technological process as the UnitedStates. While in 1956 relative sectoral productivity in Portugal were all below

16We measure aggregate output in Portugal in any given year by summing sectoral outputs in thatyear measured at the sectoral prices of the benchmark economy in 1956.17Recall from Fig. 2 and the second panel of Fig. 3 that Portugal underwent a structural transfor-mation in agriculture between 1956 and 1995 that resembles closely the structural transformationof the United States between 1870 and 1956. Hence, an alternative calibration of a would beto match the share of employment in agriculture of the United States in 1870. Normalizing theproductivity level of agriculture in 1870 to one, this would imply a = 0.48. The level of relativeproductivity in agriculture in 1956 required to match the share of employment in this sector wouldbe 4.8 or an annualized growth rate of productivity in agriculture of 1.84%. Note that this growthrate is less than half the observed growth rate of U.S. productivity in agriculture between 1956 and1995. If this level of productivity represents the frontier in the world, then Portugal in 1956 shouldhave observed a share of employment in agriculture of 10% as opposed to the 48% in the data.We conclude that Portugal is not riding along the same technological process as the United States.There are factors (either institutional or policy driven) that imply a large share of employment inagriculture in Portugal in 1956.


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Ag. DataAg. ModelInd. DataInd. ModelSvc. DataSvc. Model

Fig. 5 The structural transformation in Portugal

the US level, Portugal experienced higher annualized rates of labor produc-tivity growth in all three sectors. In this experiment, we use the growth ratesof labor productivity in agriculture, manufacturing, and services observed inPortugal between 1956 and 1995, together with the features of the two previousexperiments. The shares of employment implied by the model are plotted inPanel B of Fig. 5. The share of employment in agriculture implied by themodel matches very closely the data. This result suggests that the simplecharacterization of preferences for agricultural goods in the model representsa good abstraction of the forces for employment in agriculture relative tothe data. The share of employment in services implied by the model growsfaster than in the data, while the opposite occurs for the share of employmentin manufacturing. We conclude that there may be factors preventing themovement of people from manufacturing to services. We consider as our nextstep a barrier to the service sector summarizing all the possible forces thatprevent reallocation to services.18

18For instance, Prescott (2004) and Rogerson (2005) argue that taxes on market activities may bebehind the employment problem in European countries.


5.1.4 Barriers to services

The previous discussion implies that our simple framework does not capturethe process of labor reallocation between manufacturing and services observedin Portugal between 1956 and 1995. In this experiment, we add a time-varying barrier to the service sector so that the model matches the Portuguesestructural transformation in this period. In particular, we assume a barrier toservices πs ≥ 0 affecting wages in this sector ws

πs. Hence, from Eq. 9, we compute

this barrier to match the share of employment in manufacturing as:

πs = [Lm(1 + x) − (1 − La)] As

s.

The results of this experiment are reported in Panel C of Fig. 5. Theresulting time-varying barrier to services has the feature that it grows almostmonotonically from 1 in 1956 to 5 in 1995. The barrier can be interpreted asan increasing impact of taxes and other regulations in the service sector.19 Ourbenchmark economy with lower relative sectoral productivity in 1956, fasterproductivity growth, and a time-varying barrier to services is able to reproduceclosely the pattern of labor reallocation observed for Portugal between 1956and 1995. We use this economy as the basis of counterfactual experiments inthe next subsection.20

5.1.5 Implications for relative sectoral productivityThe model implies levels of sectoral labor productivity relative to that of theUnited States that are consistent with aggregate data. These relative sectoralproductivity are plotted in Fig. 6. The model implies that labor productivityin manufacturing in Portugal converged fast relative to that of the UnitedStates during this period, from 0.44 in 1956 to 1.1 in 1995. Labor productivity inagriculture and services in Portugal, however, experienced very limited relativeimprovement during this period: in 1956 relative productivity in agricultureand services were 0.22 and by 1995 they were 0.25 and 0.26.21

5.2 Counterfactuals

Our previous analysis suggests that productivity in agriculture and services inPortugal are behind the aggregate productivity gap with the United States. In

19See, for instance, Silva (2005) for evidence on increasing tax rates on consumption and labor inPortugal between 1970 and 2002.20While barriers to services are important to account for some features of the structural trans-formation in Portugal, we emphasize that barriers are not important in explaining the closing ofthe aggregate productivity gap with the United States. In fact, recall from Panel B in Fig. 5 that,in the absence of this barrier, employment would move faster out of manufacturing into services.Since manufacturing in Portugal is relatively more productive than services, aggregate productivitygrowth would be lower in this counterfactual situation than with the barrier.21Notice that the model imposes discipline on the relative sectoral productivity levels in 1956.Their evolution thereafter is implied by data on productivity growth by sector in each country.


1955 1960 1965 1970 1975 1980 1985 1990 19950

0.2

0.4

0.6

0.8

1

1.2

Years

Pro

duct

ivity

(P

T/U

S)

Agricuture

Industry

Services

Fig. 6 Sectoral productivity (PT/US)

this subsection, we use the model to isolate the importance of productivity ineach sector for the process of structural transformation and the evolution ofaggregate productivity in Portugal.

5.2.1 The role of manufacturing

In this counterfactual we ask about the role of productivity growth in man-ufacturing in explaining the catch up in relative aggregate productivity inPortugal between 1956 and 1995. We start from the economy that reproducesthe structural transformation in Portugal and ask how this economy wouldchange if labor productivity in manufacturing followed the path observed inthe United States (an annualized growth rate of 2.4% per year instead of4.8% in Portugal). Notice that this counterfactual situation would imply thatrelative labor productivity in manufacturing is constant at 44% during thetime period. The results of this counterfactual are reported in Fig. 7 (dashedline) and column (1) of Table 2. For comparison, Table 2 also reports theeconomy that reproduces the structural transformation for Portugal. A lowerthan observed productivity growth in manufacturing would imply more laborin manufacturing and less in services than observed in 1995. More importantly,relative aggregate productivity would be 0.38 in 1995 instead of the 0.53observed (an annualized growth of 2.8% instead of 3.7%). We conclude that


1955 1960 1965 1970 1975 1980 1985 1990 19950.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Years

Agg

rega

te P

rodu

ctiv

ity (

PT

/US

)

Benchmark

Ind. Productivity

Ag. Productivity

Svc. Productivity

Svc. & Ag. Productivity

Fig. 7 Counterfactuals on sectoral productivity (Note: These counterfactuals refer to the economythat reproduces the structural transformation in Portugal under alternative situations for sectoralproductivity. Industry productivity considers labor productivity in manufacturing as in the UnitedStates. Agriculture productivity considers a change in relative productivity in agriculture from 0.22to 0.97. Service productivity considers a change in relative productivity in services from 0.22 to 0.89.Agriculture and services productivity combines the previous two counterfactuals. See Table 2 formore details and implications.)

Table 2 Counterfactuals

(1) (2) (3) (4)Model Prod. Prod. Prod. Prod.PT industry agriculture services ag. and svc.

Labor productivity growth (%):Agriculture 4.1 4.1 7.8 4.1 7.8Industry 4.8 2.4 4.8 4.8 4.8Services 1.9 1.9 1.9 5.2 5.2

Share of employment 1995 (%):Agriculture 9.8 9.8 2.5 9.8 2.5Industry 23.4 38.1 24.1 23.7 24.9Services 66.8 52.1 73.4 66.5 72.6

Aggregate prod. (PT/US):1956 0.26 0.26 0.26 0.26 0.261995 0.53 0.38 0.54 0.89 0.95

Agg. prod. growth (%) 3.7 2.8 3.8 5.1 5.3


high labor productivity growth in manufacturing accounts for most of theaggregate productivity growth in Portugal relative to that of the United States.

5.2.2 Closing the productivity gap in agriculture

The model implies that relative productivity in agriculture in Portugal was22% in 1956 and 25% in 1995. In contrast, Rogerson (2005) suggests that theproductivity gap in agriculture between Europe (the average of the largestfour countries) and the United States required to reproduce relative laborallocations in this sector in 2000 was 0.97. We ask what the aggregate pro-ductivity implications would be of Portugal closing the productivity gap inagriculture to 0.97 by 1995. To produce this catch up, labor productivity inagriculture in Portugal would need to grow at an annual rate of 7.8% insteadof the 4.1% observed in the data. The implied shares of employment andrelative aggregate productivity are summarized in column (2) of Table 2. (Seealso Fig. 7.) Closing the productivity gap in agriculture produces an importantreallocation of employment from agriculture to services: by 1995, the share ofemployment changes from 10.5 to 2.5% in agriculture and from 67 to 73% inservices. Nevertheless, the aggregate productivity implications of this changeare relatively small: the annualized growth rate of aggregate productivitywould increase to 3.8% (compared to 3.7% in the data for Portugal) and rel-ative aggregate productivity would only increase to 0.54 (compared to 0.53 inthe data). The intuition behind this result is that while improving productivityin agriculture produces an important reallocation of labor, this reallocationshifts labor mostly towards services. As we documented previously, agricultureand services in Portugal have roughly similar relative productivity. In addition,the direct effect of the sharp improvement in agricultural productivity in theaggregate falls over time, as the associated fall in the share of employment inagriculture reduces the weight of this sector in the aggregate economy.

5.2.3 Closing the productivity gap in services

The model implies that productivity of services in Portugal relative to that ofthe United States was 22% in 1956 and 26% in 1995. In contrast, Rogerson(2005) suggests that the productivity gap in services between Europe andthe United States required to reproduce relative labor allocations in 2000 is0.89. We ask about the implications for employment allocations and aggregateproductivity of a change in relative productivity in services from 22% in 1956to 89% in 1995. This remarkable change in relative productivity generatesalmost no effect in the shares of employment across sectors. The reason isthat this improvement in productivity generates no effect in the allocationof labor in agriculture and two opposing effects in the allocation of laboracross industry and services. First, higher productivity in services relative tomanufacturing, all else equal, reallocates labor towards manufacturing dueto the low substitutability between these two goods in preferences (ρ < 0).Second, higher productivity in the production of services relative to a constants, all else equal, reallocates labor towards services. In this counterfactual, these


two opposing effects roughly cancel each other and the effects on labor allo-cations are small. However, the productivity change has an important effectin aggregate productivity because the improvement in productivity occurs in alarge and growing sector of the economy (the structural transformation). Thegrowth rate in aggregate productivity increases to 5.1% annually, leading to arelative aggregate productivity of 0.89 in 1995 as documented in the dotted linein Fig. 7 and column (3) of Table 2.

5.2.4 Closing the productivity gap in agriculture and services

We found that improving agricultural productivity by itself did not have largeaggregate productivity effects in Portugal because it reallocated labor to asector with similar initial relative productivity. However, when combined withimprovements in the productivity of the service sector, the reallocation of laborimplied by improving productivity in agriculture can amplify the aggregateproductivity effects. In this counterfactual, we combine the improvements inproductivity described in the previous two counterfactuals. As documentedin Table 2, column (4), higher productivity in agriculture implies that thereis a substantial release of labor from agriculture to services (as in the secondcounterfactual). In turn, higher relative productivity in services implies thatthis reallocation of labor has a higher aggregate effect than in the thirdcounterfactual. Relative aggregate productivity in 1995 is 0.95 compared to0.89 in the case of improvement in the service sector only. (See Fig. 7.)

5.2.5 Discussion

While manufacturing productivity accounts for most of the aggregate pro-ductivity growth in Portugal relative to that of the United States during theperiod, its role in determining aggregate productivity in the future is mitigatedby its decreasing share in employment. (Recall that Portugal has alreadystarted a second phase of structural transformation whereby employment ismoving from manufacturing to services.) Only relative productivity growth inservices can effectively provide further closing of the aggregate productivitygap with the United States. As a result, our analysis suggests that findingways of improving labor productivity in the service sector would have largeconsequences for aggregate productivity in the context of the underlyingstructural transformation.22

22In addition, in developed economies distribution services represent a substantial portion ofprices and non-agricultural intermediate inputs are used intensively in agricultural production(see Restuccia et al. 2005). As a result, low productivity in services may be partly responsiblefor low productivity in agriculture. While our model abstracted from interactions across sectors,counterfactual (4) suggests that the aggregate implications of productivity improvements inservices would be amplified if these improvements go along with productivity improvements inagriculture.


6 Conclusions

From 1956 to 1995, GDP per worker in Portugal relative to that of the UnitedStates increased from 0.26 to 0.53. This reduction of the aggregate productivitygap with the United States was associated with a process of labor reallocationacross sectors of production. In this paper, we build a general equilibriummodel of the process of structural transformation. Using this model we are ableto disentangle the role of sectoral labor productivity growth in the reductionof the aggregate productivity gap of Portugal relative to the United States. Wefind that relative labor productivity in manufacturing increased substantiallyand played an important role in this process. In turn, relative labor productivityin agriculture and services lagged behind. We show that the aggregate laborproductivity performance in Portugal hinges on closing its productivity gap inservices relative to the United States.

While our analysis is silent about the institutional and policy elementsexplaining the behavior of relative sectoral productivity, we conjecture thatdifferences in the level of competition across sectors may be responsible fortheir diverse performance. One possible source for differences in the level ofcompetition across sectors is the degree of foreign competition. In particular,manufacturing goods are typically tradable while service goods (and, to alesser extent, agricultural goods) are typically non-tradable. Therefore, foreigncompetition brought about by growth policies that promote trade tend to havea bigger impact on the structure of the manufacturing sector. In contrast, theinstitutional environment of the service sector cannot rely solely on foreigncompetition. Promoting labor productivity in the service sector requires poli-cies that lower product-market regulation and barriers to entry that appear tobe pervasive in this sector. To the extent that services constitute a large andincreasing sector of the economy, it is important to understand the sourcesof productivity growth in services and the institutional environment that canpromote it. We leave this relevant task for future research.

Appendix A: Data sources and definitions

Aggregate data We use annual data on aggregate GDP per worker for theUnited States and Portugal from Heston et al. (2002), also known as the PennWorld Tables Version 6.1 (PWT6.1).

Sectoral data We adopt the following sectoral definitions: Agriculture com-prises agriculture, forestry, and fishing; Industry comprises mining, manufac-turing, public utilities, and construction; and Services includes wholesale andretail trade; transport and communication; finance, insurance, and real estate;community, social, and personal services; and government services. For theUnited States, we obtain data on employment by sector from 1869 to 1970from the U.S. Census Bureau, Department of Commerce (1975), HistoricalStatistics of the United States. For the period 1956–1995, we obtain annual


data for employment by sector from the OECD Employment Database (2005)and annual data for value added by sector from the Conference Board andGroningen Growth and Development Centre (2005), 10-Sector Database. ForPortugal, we obtain annual data on employment by sector and value addedby sector for the period 1956–1995 from Banco de Portugal (2005), SériesLongas para a Economia Portuguesa. For both the United States and Portugal,we compute labor productivity by sector as the ratio of value added toemployment. However, it is not generally the case that the growth in aggregatelabor productivity implied by the sectoral measures matches the growth inlabor productivity from PWT6.1. Therefore, we adjust labor productivity ina sector by the ratio of the share of value added to the share of employment inthat sector.

Smoothed data All series (except the historical shares of employment in theUnited States) are smoothed by applying the Hodrick–Prescott filter to the logof each series with a smoothing parameter λ = 100.

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